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Geodetic Observations of Weak Determinism in Rupture Evolution of Large Earthquakes.
The moment evolution of large earthquakes is a subject of fundamental interest to both basic and applied seismology. Specifically, an open problem is when in the rupture process a large earthquake exhibits features dissimilar from those of a lesser magnitude event. The answer to this question is of importance for rapid, reliable estimation of earthquake magnitude, a major priority of earthquake and tsunami early warning systems. Much effort has been made to test whether earthquakes are deterministic, meaning that observations in the first few seconds of rupture can be used to predict the final rupture extent. However, results have been inconclusive, especially for large earthquakes greater than M w 7. Traditional seismic methods struggle to rapidly distinguish the size of large-magnitude events, in particular near the source, even after rupture completion, making them insufficient to resolve the question of predictive rupture behavior. Displacements derived from Global Navigation Satellite System data can accurately estimate magnitude in real time, even for the largest earthquakes. We employ a combination of seismic and geodetic (Global Navigation Satellite System) data to investigate early rupture metrics, to determine whether observational data support deterministic rupture behavior. We find that while the earliest metrics (~5 s of data) are not enough to infer final earthquake magnitude, accurate estimates are possible within the first tens of seconds, prior to rupture completion, suggesting a weak determinism. We discuss the implications for earthquake source physics and rupture evolution and address recommendations for earthquake and tsunami early warning
Learning Convex Partitions and Computing Game-theoretic Equilibria from Best Response Queries
Suppose that an -simplex is partitioned into convex regions having
disjoint interiors and distinct labels, and we may learn the label of any point
by querying it. The learning objective is to know, for any point in the
simplex, a label that occurs within some distance from that point.
We present two algorithms for this task: Constant-Dimension Generalised Binary
Search (CD-GBS), which for constant uses queries, and Constant-Region Generalised Binary
Search (CR-GBS), which uses CD-GBS as a subroutine and for constant uses
queries.
We show via Kakutani's fixed-point theorem that these algorithms provide
bounds on the best-response query complexity of computing approximate
well-supported equilibria of bimatrix games in which one of the players has a
constant number of pure strategies. We also partially extend our results to
games with multiple players, establishing further query complexity bounds for
computing approximate well-supported equilibria in this setting.Comment: 38 pages, 7 figures, second version strengthens lower bound in
Theorem 6, adds footnotes with additional comments and fixes typo
Efficient Implementation of a Synchronous Parallel Push-Relabel Algorithm
Motivated by the observation that FIFO-based push-relabel algorithms are able
to outperform highest label-based variants on modern, large maximum flow
problem instances, we introduce an efficient implementation of the algorithm
that uses coarse-grained parallelism to avoid the problems of existing parallel
approaches. We demonstrate good relative and absolute speedups of our algorithm
on a set of large graph instances taken from real-world applications. On a
modern 40-core machine, our parallel implementation outperforms existing
sequential implementations by up to a factor of 12 and other parallel
implementations by factors of up to 3
Chimera and globally clustered chimera: Impact of time delay
Following a short report of our preliminary results [Phys. Rev. E 79,
055203(R) (2009)], we present a more detailed study of the effects of coupling
delay in diffusively coupled phase oscillator populations. We find that
coupling delay induces chimera and globally clustered chimera (GCC) states in
delay coupled populations. We show the existence of multi-clustered states that
act as link between the chimera and the GCC states. A stable GCC state goes
through a variety of GCC states, namely periodic, aperiodic, long-- and
short--period breathers and becomes unstable GCC leading to global
synchronization in the system, on increasing time delay. We provide numerical
evidence and theoretical explanations for the above results and discuss
possible applications of the observed phenomena.Comment: 10 pages, 10 figures, Accepted in Phys. Rev.
An Empirical Study of Finding Approximate Equilibria in Bimatrix Games
While there have been a number of studies about the efficacy of methods to
find exact Nash equilibria in bimatrix games, there has been little empirical
work on finding approximate Nash equilibria. Here we provide such a study that
compares a number of approximation methods and exact methods. In particular, we
explore the trade-off between the quality of approximate equilibrium and the
required running time to find one. We found that the existing library GAMUT,
which has been the de facto standard that has been used to test exact methods,
is insufficient as a test bed for approximation methods since many of its games
have pure equilibria or other easy-to-find good approximate equilibria. We
extend the breadth and depth of our study by including new interesting families
of bimatrix games, and studying bimatrix games upto size .
Finally, we provide new close-to-worst-case examples for the best-performing
algorithms for finding approximate Nash equilibria
Globally clustered chimera states in delay--coupled populations
We have identified the existence of globally clustered chimera states in
delay coupled oscillator populations and find that these states can breathe
periodically, aperiodically and become unstable depending upon the value of
coupling delay. We also find that the coupling delay induces frequency
suppression in the desynchronized group. We provide numerical evidence and
theoretical explanations for the above results and discuss possible
applications of the observed phenomena.Comment: Accepted in Phys. Rev. E as a Rapid Communicatio
The Inverse Shapley Value Problem
For a weighted voting scheme used by voters to choose between two
candidates, the \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of
provide a measure of how much control each voter can exert over the overall
outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley
and Martin Shubik in 1954 \cite{SS54} and are widely studied in social choice
theory as a measure of the "influence" of voters. The \emph{Inverse Shapley
Value Problem} is the problem of designing a weighted voting scheme which
(approximately) achieves a desired input vector of values for the
Shapley-Shubik indices. Despite much interest in this problem no provably
correct and efficient algorithm was known prior to our work.
We give the first efficient algorithm with provable performance guarantees
for the Inverse Shapley Value Problem. For any constant \eps > 0 our
algorithm runs in fixed poly time (the degree of the polynomial is
independent of \eps) and has the following performance guarantee: given as
input a vector of desired Shapley values, if any "reasonable" weighted voting
scheme (roughly, one in which the threshold is not too skewed) approximately
matches the desired vector of values to within some small error, then our
algorithm explicitly outputs a weighted voting scheme that achieves this vector
of Shapley values to within error \eps. If there is a "reasonable" voting
scheme in which all voting weights are integers at most \poly(n) that
approximately achieves the desired Shapley values, then our algorithm runs in
time \poly(n) and outputs a weighted voting scheme that achieves the target
vector of Shapley values to within error $\eps=n^{-1/8}.
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